arXiv:math/0404075 Abstract

arXiv:math/0404075 [math.GR]Abstract References Reviews Resources

Algebraic entropy of elementary amenable groups

Published 2004-04-05Version 1

We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of uniformly exponential growth. We also show that 0 is an accumulation point of the set of entropies of elementary amenable groups.

Comments: 20 pages; to appear in Geom. Dedicata

Categories: math.GR

Subjects: 20F65, 20F69

Keywords: algebraic entropy, finitely generated elementary amenable group, finite index, nilpotent subgroup, entropy contains

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